# Cartesian rotation vector

Hi AnyBody Team,

I’ve a question about the Cartesian rotation vector. In the RefManual,
the explanation sounds like the helical axis theorem but the real
behaviour appears to be more like using Roll-Pitch-Yaw angles.
Could you please explain the Cartesian rotation vector in more detail
or give me some hints for finding more information in the net?

What does the remark in the RefManual mean: “It must be emphasized that
the velocity of the rotation vector is not equal to the angular velocity
vector, except in the planar case where the axis of rotation is
constant.”

Is it really a problem when doing an invers-dynamic analysis?

Thanks a lot in advance,
Tim

Hi Tim

You are right about the Helical axis theorem, the Cartesian rotation vector
(Type=Rotvector) is very much like this, but it does not capture the
translation. The rotation alone is described as a vector in 3D where the
rotation can be done by a single rotation about the axis of the vector and
the length of vector gives the magnitude of the rotation (rad).

I am unsure why you mean that it behaves more like the CardanAngles (Type=
RotAxesAngles) this is what you mean by Roll-pitch-yaw right? Please give an
example of this?

For small angles, I guess, they will look much the same.

The remark about the angular velocity and the planar case is meant to avoid
typical confusion. The angular velocity (often referred to as vector omega)
is a velocity measure (a geometrical vector point in the instant axis of
rotation and the length is the magnitude of the angular velocity). No set of
3D rotational coordinates can, in general, be differentiated in time to
provide the omega vector; there is always a need for some transformation
between the time-derivatives of the rotational positions in order to get
omega and visa versa.

The Cartesian Rotation Vector (being composed as a geometrical vector of the
axis and magnitude of the angle) can easily lead to think that it is in fact
the matching the omega vector with almost the same description, but in
general it does not. It does only match if you keep the axis of rotation
constant for all times, i.e. a planar rotation about the constant axis.

I hope this makes sense

Best regards

SÃ¸ren, AnyBody Support

From: anyscript@yahoogroups.com [mailto:anyscript@yahoogroups.com] On Behalf
Of timwehner
Sent: 30 September 2008 16:29
To: anyscript@yahoogroups.com
Subject: [AnyScript] Cartesian rotation vector

Hi AnyBody Team,

I’ve a question about the Cartesian rotation vector. In the RefManual,
the explanation sounds like the helical axis theorem but the real
behaviour appears to be more like using Roll-Pitch-Yaw angles.
Could you please explain the Cartesian rotation vector in more detail
or give me some hints for finding more information in the net?

What does the remark in the RefManual mean: “It must be emphasized that
the velocity of the rotation vector is not equal to the angular velocity
vector, except in the planar case where the axis of rotation is
constant.”

Is it really a problem when doing an invers-dynamic analysis?

Thanks a lot in advance,
Tim

[Non-text portions of this message have been removed]